Pipe Poiseuille flow of viscously anisotropic, partially molten rock

TL;DR

This paper models pipe Poiseuille flow of partially molten, viscously anisotropic rock to predict melt segregation patterns, providing baseline results for future laboratory experiments on mantle dynamics.

Contribution

It introduces a new model of pipe Poiseuille flow with anisotropic viscosity, extending previous plane flow models and offering predictions for melt behavior in laboratory settings.

Findings

Melt migrates from the pipe center to the wall.

High-porosity bands form near the wall at low angles.

Radially varying anisotropy improves model self-consistency.

Abstract

Laboratory experiments in which synthetic, partially molten rock is subjected to forced deformation provide a context for testing hypotheses about the dynamics and rheology of the mantle. Here our hypothesis is that the aggregate viscosity of partially molten mantle is anisotropic, and that this anisotropy arises from deviatoric stresses in the rock matrix. We formulate a model of pipe Poiseuille flow based on theory by Takei and Holtzman [2009a] and Takei and Katz [2013]. Pipe Poiseuille is a configuration that is accessible to laboratory experimentation but for which there are no published results. We analyse the model system through linearised analysis and numerical simulations. This analysis predicts two modes of melt segregation: migration of melt from the centre of the pipe toward the wall and localisation of melt into high-porosity bands that emerge near the wall, at a low angle to the shear plane. We compare our results to those of Takei and Katz [2013] for plane Poiseuille flow; we also describe a new approximation of radially varying anisotropy that improves the self-consistency of models over those of Takei and Katz [2013]. This study provides a set of baseline, quantitative predictions to compare with future laboratory experiments on forced pipe Poiseuille flow of partially molten mantle.